The Council may grant to any individual, company, or corporation operating a public utility, the right to extend the appliance and service of such utility. All such extensions shall become a part of the aggregate property of the utility by virtue of the ordinance providing for its construction and operation, and shall thereafter be subject to all the terms, conditions, and provisions of the original grant. The right to use and maintain any such extension shall expire with the original grant of the utility to which the extension was made or any renewal thereof.